Digital modulation systems use a finite number of distinct signals to represent digital data. Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). PSK systems use a finite number of phases, each assigned a unique pattern of binary bits. Each pattern of bits forms a symbol that is represented by the particular phase. A demodulator, which is designed for the symbol-set used by a modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering original data. This requires the receiver to be able to compare the phase of a received signal to a reference signal.
Alternatively, instead of using the bit patterns to set the phase of a wave, a PSK system can instead change the phase of the wave by a specified amount. The demodulator determines the changes in the phase of a received signal rather than the phase itself. Since such a system relies on the difference between successive phases, it is termed differential PSK (DPSK). DPSK can be significantly simpler to implement than ordinary PSK since there is no need for the demodulator to have a copy of the reference signal to determine the exact phase of the received signal (it is a non-coherent scheme), but produces more erroneous demodulations.
Binary PSK (BPSK) uses two phases which are separated by 180°. Constellation points can be treated as if at 0° and 180° on an axis because it does not particularly matter exactly where the constellation points are positioned. Variations include quadrature PSK (QPSK), offset QPSK (OQPSK), π/4-QPSK, higher order PSK, etc.
Quadrature amplitude modulation (QAM) is both an analog and a digital modulation scheme. QAM conveys two analog message signals, or two digital bit streams, by modulating the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. These two waves are out of phase with each other by 90° and are thus called quadrature carriers or quadrature components. The modulated waves are summed, and the resulting waveform is a combination of both PSK and amplitude-shift keying, or in the analog case of phase modulation (PM) and AM. In the digital QAM case, a finite number of at least two phases and at least two amplitudes are used. PSK modulators are often designed using the QAM principle, but are not considered as QAM since the amplitude of the modulated carrier signal is constant.
A low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel, and is constructed using a sparse bipartite graph. LDPC codes are capacity-approaching codes, which means that practical constructions exist that allow a noise threshold to be set very close to the theoretical maximum (the Shannon limit) for a memory-less channel. The noise threshold defines an upper bound for the channel noise up to which the probability of lost information can be made as small as desired. Using iterative belief propagation techniques, LDPC codes can be decoded in time linear to their block length. Low Density Parity Check Codes, Number 21 in Research monograph series, R. Gallager, 1963—MIT Press, Cambridge, Mass. is incorporated by reference.